Least Common Multiple (LCM) of 57 and 157
The least common multiple (LCM) of 57 and 157 is 8949.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 57 and 157?
First, calculate the GCD of 57 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 157 = 0 remainder 57 |
| 2 | 157 ÷ 57 = 2 remainder 43 |
| 3 | 57 ÷ 43 = 1 remainder 14 |
| 4 | 43 ÷ 14 = 3 remainder 1 |
| 5 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 103 | 6901 |
| 14 and 115 | 1610 |
| 198 and 106 | 10494 |
| 139 and 199 | 27661 |
| 48 and 173 | 8304 |